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Summary: Computing 70, 235-259 (2003)
Digital Objeet Identifier (001) 10.1007/s00607-003-00l4-6 Computing
Printed in Austria
Iterative Methods for Linear Complementarity
Problems with Interval Data*
G. Alefeldand U. Schäfer, Karlsruhe
Reeeived Oetober 7, 2002; revised April 15, 2003
Published online: June 23, 2003
@ Springer-Verlag 2003
Abstract
In this paper we introduee the total step method, the single step method and the symmetrie single step
method for linear eomplementarity problems with interval data. They are applied to an interval matrix
[A] and an interval veetor [b]. If all A E [A] are H-matrices with positive diagonal elements, these
methods are all eonvergent to the same interval veetor [x*].This interval vector indudes the solution x
of the linear complementarity problem defined by any fixed A E [A]and any fixed b E [b].If all A E [A]
are M-matrices, then we will show, that [x*]is optimal in a precisely defined sense. We also consider
modifications of those methods, whieh under eertain assumptions on the starting vector deliver nested
sequences converging to [x*].We dose our paper with some examples which illustrate our theoretical
results.
AMS Subject Classifications: 90C33, 65G30.
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